Civil Engineering Reference
In-Depth Information
dynamic mid-span deflection and associated impact factor for a 45 ft long
ballasted deck through plate girder span traversed by a single concentrated
load of 400 kips moving at 70 mph (103 ft/s) on a smooth surface. The span
weighs150,000 lb(totaldeadloadincludingballasteddeck)andhasamoment
of inertia of 96,000 in.
4
.
150,000
32.17
(
45
)
=
103.6 lb-s
2
/
ft
2
,
m
=
(
29
E
6
)(
96,000
)
(
103.6
)(
144
)
2
(
45
)
2
π
ω
1
=
=
66.58 rad
/
s,
2
π
ω
1
=
T
1
=
0.094 s,
π
V
L
π
(
103
)
45
=
=
7.19 rad
/
s.
0.44 s, is
greaterthanone-halfthespanperiod,
T
1
/
2;therefore,themaximumresponse
will occur when the moving load is on the spa
n
. The maximum forced
vibrationmid-spandeflectionfromEquation4.13is
y(L/
2,
t)
=
The duration of the forcing function pulse,
L/V
=
45
/(
103
)
=
−
mum dynamic mid-span deflection is 0.50 in. The maximum static mid-span
deflection is
0.47
(
sin 7.19
t
PL
3
48
EI
=
0.47 inches.
The impact factor is, then, 0.50
/
0.47
=
1.06 (i.e., increase static forces by 6%
to account for dynamic effects).
This impact factor would not be appropriate for design considering the
assumptions made during the development of the equation of motion and
its subsequent solutions. This is why impact measurements taken on actual
bridges show appreciably greater impacts for the reasons discussed later in
this section.
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
Time (
t
)
0.3
0.4
FIGURE E4.4
